Stores vs. Random Number God
Stores have random items in them, so it is important to know which ones will be most important to buy. From rarest (and therefore highest priority) to most common, the order is

1) Augments
Augments are number one simply due to how valuable they are. They are by far the best way to upgrade your ship and are a huge force multiplier. Scrap Recovery Arm and Long Range Scanner are useful to everyone, Weapons Reloader and Weapons Pre-igniter are useful to weapons-based ships, Stealth Weapons are useful for Weapon-based ships that have cloak, Drone Recovery Arm is useful for drone users, and Repair Arm should never be bought.

2) Weapons
Weapons are rare and diverse enough that what you find will likely dictate which direction your build goes. Between Lasers vs. Beams vs. Missiles vs. Bombs and Damage vs. Fire. vs. Ion vs. System subtypes, finding a weapon that works with what you already have is extremely useful.

3) Crew
Random encounters where you can get crew members are moderately common, but this is the only time where you can get specific crew. Since each different race unlocks various blue options in encounters, rounding out your roster here is very useful.

4) Subsystems
Subsystems are as much of a game changer as Augmentations. However they are more of an investment with the initial cost plus the upgrades and increased power requirements. The good news is that there are only a few subsystems you can buy and a lot of stores of subsystems so you can afford to wait until later to buy the system you want.

5) Drones
There are only a few different types of drones, so you can usually find one that is helpful. Drones are mostly for support anyway, so this isn’t as important as the rest.

6) Fuel/Missiles/Drone Parts/Repair
Every station has them. Buy what you need, but there’s not much reason to really stock up.

There are three ways to defend: Shields, Evade, and Defense Drones. As you can see, Evade defends against the most, followed by shield, followed by drones. First upgrade should be shields as that’s more certain, but make sure engines are upgraded as well. The computer beams randomly into your ship so one level of doors is mandatory as well.

When attacking, you need something that beats a high shield/evade score. Lasers can whittle down high shields if you have a lot of them and fire in a volley, but that greatly lowers your damage and you have to choose between disabling weapons and shields. Ideally you also want something that can bypass shields entirely. Blast doors aren’t a factor for transporters since you can beam directly into the room you want to destroy. Bombs are better than missiles since they can’t be shot down.

Take out their ability to damage you first, unless you have problems dealing damage, then take out shields/engine then weapons/drones/transporter. Killing the crew requires upgraded sensors and either specialized weapons or a good boarding party, preferably both. Don’t go for it unless you are properly equipped.

Slaying the Random Number God
Many Blue options are triggered when you have a specific race in your crew. Ion weapons also trigger a few blue events, as well as an upgraded medical bay. The more blue options you can get, the less the Random Number God can screw you over.

Long Range Scanners means never having to jump into the sun.

Never pick options that risk losing crew. They can be difficult to replace.

Boarding actions are less random than using weapons, but they are not completely without risk. If your transporter takes a hit or the enemy cloaks or jumps out when your party is away, things can become very bad. Make sure you use scanners to scout ahead and recall your crew at the first sign of trouble.

Taking out the enemy helm prevents them from evading, and prevents the Random Number God from making you miss 6 shots out of a volley of 7.

On the flip side, the no matter your evade you will eventually be hit. Make sure you get shield upgrades and keep them running.